Consensus Control And Optimization Of The Multi-Agent Systems

In recent years, multi-agent systems have found widely engineering applications in such areas as energy management and optimization in microgrids, demand response management in microgrids, fault diagnosis and congestion control in wireless sensor networks, attitude regulation of unmanned vehicles, unmanned driving systems. The theoretical foundation of such applications is consensus. This thesis focuses on consensus control of multi-agents and its application in distributed optimization. The main contributions and originalities in this thesis are listed as follows:1 The research background and significance of multi-agents are introduced. Meanwhile, the main contributions in this thesis are briefly outlined.2 Leader-following consensus of second-order multi-agent systems with uniform sampled-data control is considered. By designing the controller that contains the real-time position and velocity information as well as the sampled position and velocity information, then employing the algebra graph theory and linear system theory, necessary and sufficient conditions are obtained to ensure the second-order consensus. The criteria show that the second-order consensus can be reached if and only if the sampling period and coupling gains satisfy several algebraic inequalities. Finally, two numerical examples are illustrated to show the effectiveness and the correctness of the theoretical analysis in this chapter.3 Event-based semi-global leader-following consensus of general linear multi-agent systems is considered. The multi-agent systems considered in this chapter contain input saturations. By employing algebraic graph theory, M-matrix theory and Lyapunov method, two classes of event-based sampling controllers are designed, one is the event-triggered sampling controller that depends on continuous-time communications among the agents;the other is the self-triggered sampling controller that depends on discrete-time communications. For such two classes of event-based controllers, under the assumption that the leader agent is globally reachable, the algebraic inequalities based criteria are obtained to ensure the semi-global leader-following consensus, respectively. Moreover, the inter-event times for such two classes of event-based controllers are proved to be positively lower bounded, respectively, i.e., the Zeno behavior can be excluded. Finally, two numerical examples are illustrated to show the effectiveness of the theoretical analysis in this chapter.4 Constrained consensus of asynchronous discrete-time multi-agent systems is considered, where each agent needs to lie in a closed convex constraint set while reaching consensus. In order to deal with the asynchronous information exchange that is induced by asynchronous communication, the ``non-computing’’ agents are added to the original multi-agents such that the original asynchronous multi-agent system can be equivalently transformed to the synchronous multi-agent system. For the multi-agent systems with synchronous communications, by employing the properties of projection operator on the convex set and the properties of the state transition matrix, the linear parts of the newly constructed systems are proved to converge, and their nonlinear parts are proved to vanish over time, which means that the constrained consensus of the original systems can be reached. Finally, two numerical examples are illustrated to show the effectiveness of the theoretical analysis in this chapter.5 The distributed multi-agent optimization with inequality constraints and random projections is considered. The global objective function of the convex optimization problem is composed by several convex sub-objective functions, and the constraint conditions include by the global inequality constraint and randomly occurring state constraint sets. In order to deal with this problem, the distributed multi-agent primal-dual random projection subgradient algorithm is proposed. This algorithm is composed by two parts: the information fusion part and counter-subgradient descent part. In the information fusion part, the agents fuse the information among their own and their neighbors’ by weighted averaging. In the counter-subgradient descent part, the agents choose the counter-subgradient direction of the local Lagrange function as the descent direction, then combining the searching stepsize to update the states. By employing iterative inequality techniques and the convex optimization theory, the consensus of the proposed algorithm with diminishing stepsize is proved, which means that the states of the agents converge to the optimal solution of the convex optimization problem. Finally, a numerical example is illustrated to show the effectiveness of the theoretical analysis in this chapter.